In medicine, there are some diseases that have complicated nature and should be analysed deeply in order to provide the patient with the right treatment. Among these diseases that can lead to death, or disability are the cerebrovascular diseases. These types of diseases commonly occur due to the dysfunction of the blood vessels supplying the brain. There are different kinds of cerebrovascular diseases including aneurysms, strokes, arteriovenous malformation, and carotid stenosis. Haemorrhage, a cerebrovascular disease, is considered a cause for strokes for almost 20% of the cases. Furthermore, cerebrovascular diseases are considered the third leading cause of death and disability. For neurosurgeons, analysing the brain scans manually takes a long time and a lot of effort especially when tracking a small vessel in the orthogonal view in order to be able to get a better picture of the vascular anatomy. With the aid of bio-engineers and computer engineers, several computer aided diagnostic (CAD) systems have been developed to analyse cerebrovascular structures, taking into consideration that any CAD system needs accurate segmentation of the cerebrovasculature from the surroundings, and this is the main motivation behind developing our approach.
Several modalities have been used for non-invasive vascular imaging e.g., computed tomography angiography (CTA) and magnetic resonance angiography (MRA). The three commonly used MRA techniques are Time-of-Flight MRA (TOF-MRA), phase contrast angiography (PCA), and contrast enhanced MRA (CE-MRA). Both TOF-MRA and PCA use flowing blood as an inherent contrast medium, while for CE-MRA a contrasting substance is injected into the circulatory system. PCA exploits phase changes of transverse magnetization when flowing spins move through a magnetic field gradient. This provides good background signal suppression and can quantify flow velocity vectors for each voxel. TOF-MRA relying on amplitude differences in longitudinal magnetization between flowing static spins is less quantitative, however it is fast and provides high contrast images. The fact that it is widely used in clinical practice is another motivation behind our work. An overview of the most recent approaches for vascular segmentation will be given below, focusing on cerebrovascular approaches using MRA, which are mainly categorized in literature into scalespace filtering, centerline-based, deformable, statistical, and hybrid models.
Multiscale filters improve the curvilinear structures in 3D medical imaging by using multiple scales to convolve an image with Gaussian filters. Moreover, analyzing the eigenvalues of the Hessian for each voxel determines the 3D structures local shapes. The output of the multiscale filtering represents a new enhanced image in a manner that makes curvilinear structures look brighter while other components look darker. A multiscale-based approach was proposed in a prior art in which Markov marked point processes are used for extracting coronary arteries in 2D X-ray angiograms. The Coronary vessels are locally modelled as piece-wise linear segments of variable widths, lengths, locations, and orientations. A Markov object process based on a uniform Poisson process is used to extract the centerlines of the vessels. In order to optimize the process, simulated annealing is done using a reversible Markov chain Monto Carlo technique.
Minimal path centerline-based approaches formulate the extraction of the centerline using 2 points as the minimum cost integrated across the path of the centerline. The centerlines of blood vessels were extracted by G{umlaut over ( )} uls {umlaut over ( )}un and Tek by computing the graph edge cost in the direction of the minimal path using medialness multiscale filtering. The centerline of the full vessel tree was then extracted using a post processing algorithm based on the centerlines scale and length. Furthermore, another prior art proposed a framework for extracting the tubular structures automatically from 2D images using the shortest paths. They merged orientation and multiscale optimization for the 4D paths to be propagated on the 2D images, where 4D refers to the combination of scale, space and orientation. Minimal path approaches could result in shortcut problems by tracking a false straight path instead of the true curve. This problem was handled by traditional methods, which segmented the coronary arteries using a minimum average-cost path.
For deformable models based segmentation techniques or active contour models (ACM), they mainly tend to find an estimate of the blood vessels boundary surface. The surface energy is optimized by the evolution of an initial boundary (snake). This is dependent on the smoothness of the surface, in addition to the image gradients. Traditional systems developed a maximum intensity projection (MIP) active contour based approach for cerebrovascular segmentation. Their method projects the brain into 2D space where an integrated ACM is applied, and the output is then converted back into 3D. Although the results of this method were very promising, it is complicated as it requires a lot of projections. To segment complex objects and obtain the energy function, it is preferable to consider both the region information and boundary information. A hybrid level-set (HLS) has been previously proposed by prior art for brain segmentation. A threshold value was set which represented the lower gray boundary so the algorithm will only extract the image parts with a gray level that is higher than the defined threshold. However, the used threshold value was constant which cannot fit different intensity distributions. Hong et al. proposed a localized hybrid level-set (LLS) that calculates the dynamic threshold locally for the targeted object in the image. Their method was found to segment small vessels more effectively but loses the information in the thick parts. Thus, the HLS was more effective in segmenting thick vessels but not in tiny vessels, whereas the LLS was more effective in extracting tiny vessels.
When comparing deformable models to scale space filtering, deformable models give better results, however they might require some human interaction represented in the initialization. Also, it is worth mentioning that deformable models and scale space filtering are slower than statistical methods.
Statistical approaches for extracting blood vessels are automatic, however the accuracy depends on the probability models being involved. The MRA scans can be considered multimodal as the intensities of each region are accompanied with a specific dominant mode of the intensity total marginal probability distribution. For adaptive statistical vascular segmentation approaches, they were introduced by prior art for TOF-MRA for PC-MRA. In the marginal data distribution was represented with a mixture of 2 Gaussians in addition to a uniform component, corresponding respectively to brain tissues, cerebrospinal fluid, and arteries, while Rician distributions were used in instead of Gaussians. Both approaches made use of a conventional expectation maximization (EM) algorithm in order to estimate the parameters of the mixture. Such EM algorithm was modified in by using the marginal grey level distribution instead of the actual grey levels. This modification has been commonly known for density estimation.
Various hybrid techniques worked on combining the previously mentioned techniques. As an example, prior art combined shape information and signal statistics to derive a region-based deformable contour to segment tubes. Furthermore, geometry of surfaces and second order statistics were used by prior art to guide a deformable model surface for the purpose of vascular segmentation in PC-MRA and TOF-MRA. Traditional systems proposed a method based on a Rayleigh-Gaussian mixture model. In their method, when analyzing the histogram, many nonvascular voxels are removed, therefore, this problem can be avoided by dividing the voxels based on their region where vascular voxels are in regions with high intensity and non-vascular voxels are found in the low intensity regions. Prior art proposed a segmentation method that was based on Markov random field (MRF) and particle swarm optimization (PSO) algorithms. In addition, a new finite mixture mode with two Gaussian and one Rayleigh distributions used for the intensity histogram of brain tissues in medical image. Traditional methods presented a cerebrovascular segmentation framework from TOF-MRA that combines statistical, deformable and scale-space techniques. In these methods, they calculated the vesselness and then used fuzzy logic to combine it with the TOF-MRA data.
This was then used to initialize a level-set technique. This work was extended by prior art by modifying the vesselness function to include multiscaling in order to handle different vascular sizes. Moreover, a traditional system proposed a framework for segmenting cerebral vessels from MRA using gradient information and statistics.
In summary, traditional methods demonstrate the following limitations:                Most of them are semiautomatic which require user interaction to initialize a vessel of interest, in particular, the deformable based segmentation approaches.        Some of them developed their approaches based on an assumption the vessels follow tubular shape; this holds for healthy people but not for patients with stenosis or an aneurysm.        Most of them are developed based on using pretrained models and did not take into account any features from the given data to make their approach adaptable and not biased to the training data.        